Description of VLSM

There are five modules in VLSM dedicated to the topics covered in the Statics course. The titleof each module along with a sample of topics covered within it are shown in Table 1 below.

Table 1. Description of Statics modules and samples of corresponding topics

Module Sample of Topics

1. Concurrent Force SystemsTrigonometry; Analytic geometry; Vectors;Force resultant; Newton’s laws; Free-bodydiagram and equilibrium of particles under 2-or 3-dimensional loading condition

2. Non-Concurrent Force Systems

Distributed forces; Moments about a point andaxis; Rigid supports; Free-body diagram andequilibrium of rigid bodies under 2- or 3-dimensional loading condition

3. Trusses, Frames, and Machines Analysis of plane trusses, frames and machines

4. FrictionStatic and kinetic friction; Single- and multi-body contact problems

5. Geometric Properties of ShapesCentroid; Center of gravity; Area and massmoments of inertia; Radius of gyration

VLSM is designed to be learner-centered with a presentation style that demystifies the conceptsmany students find difficult to understand and to learn. It contains elements that highlight therelevance of course material to students in all engineering disciplines but more so to those inaerospace, biological, civil, and mechanical engineering. Its various features are designed tosupport almost all learning styles.

Among students who take Statics, some start with a weak foundation of prerequisite topics intrigonometry, calculus, and physics. Consequently, they tend to quickly fall behind their peersand do poorly in the course. In response to this problem, several sections in Module 1 aredevoted entirely to the discussion of mathematics essential in developing the student’s ability towork various problems discussed in the Statics course.

Each module has a main page similar to that shown in Fig. 1 with the corresponding table ofcontents shown in the left frame. The user can select any item on that list and see thecorresponding content appear in the right frame.

• Frequently-Asked Questions

In all modules, the first item that appears in the left frame is a question. This is done toimmediately engage the student in thinking about the topics he/she is about to study. Thisquestion is then followed by a list of other frequently asked questions and answers. Dependingon the nature of a question, the answer is given either in textual form or in combination withfigures and equations. The collection of questions—asked by former students—are used to formthe initial list with continuous updates and expansion over time.

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Fig. 1 View of the main page of the Non-Concurrent Force Systems module

• Tutorial Discussions

These discussions elaborate on specific topics in each module. They use a blend of text, figures,mathematical expressions, and in some cases interactive models and demonstrations. Theinteractive models are developed using the Macromedia’s Flash/Shockwave software. They aredesigned to provide a vivid depiction of concepts that students find difficult to visualize andunderstand from still photos/drawings or textual descriptions found in most textbooks. Thevisual, and interactive features make the tutorial discussions particularly attractive to sensing,visual, and active learners. Figure 2 shows the tutorial discussion about the rigid supports. Byclicking on a particular support, a new window appears. By clicking on the animate button, thegeneral motion allowed by the support is animated and the free-body diagram of the connectedmember with reaction forces and possibly moments are drawn. There are a total of 20 animationor interactive models in the Statics modules of VLSM.

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Fig. 2 Discussion of the rigid supports in the Non-Concurrent Force Systems module

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• “Textbook-Style” Example Problems

These example problems demonstrate the analysis process and the application of solutiontechniques in a methodical and step-by-step fashion. However, unlike most textbooks, theseexamples describe all the intermediate steps and provide more explanations for various steps inthe solution process, as shown in Fig. 3.

Fig. 3 An example problem in the Non-Concurrent Force Systems module

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While helpful to all, these examples are more appealing to sensing, visual, verbal, sequential, andreflective learners. The Statics modules of VLSM contain 43 such example problems.

• LiveMath Example Problems

These example problems differ from those in the previous group as they were developed usingthe Theorist Interactive’s symbolic mathematical software LiveMath®. Although initially thesolution is based on the data specified in the problem statement, LiveMath makes it possible forthe user to alter the data directly from the browser window and immediately witness the changesreflected in every step of the solution as well as in the accompanying 3-dimensional graph, asshown in Fig. 4.

The ability to change the data allowsstudents to solve multiple problemsbased on a single LiveMath example.Students can, therefore, experimentwith various “what if” scenarios. Theability to interact with the graph (e.g.,rotate and zoom) enhances thevisualization and understanding of theproblem and its solution. Theseexample problems are especiallyhelpful to active, visual, and sensinglearners. The Statics modules ofVLSM contain 22 LiveMath exampleproblems.

Fig. 4 A LiveMath example problem in the Concurrent Force Systems module

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• Test-Your-Knowledge Exercises

In each test-your-knowledge exercise, as shown in Fig. 5, the student is asked to solve aparticular problem and to input one or more numerical answers. When an answer is correct(within a specified margin of accuracy), the system responds with a positive message. Moreimportantly, when an answer is wrong, the system responds with a hint as well as a link to thediscussion that deals with topics related to that problem.

Fig. 5 A test-your-knowledge exercise in the Trusses, Frames, and Machines module

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In each exercise, the student is given multiple opportunities to input an answer but will receivehints for up to three attempts. Each hint provides more helpful suggestions than the previous onewith the final hint also containing a link to the solution. The hints in each exercise are based ona predetermined set of responses and do not involve artificial intelligence. The intent of theseexercises is not to assign grades but to encourage students to improve their skills andcompetency in analysis of various problems and in application of solution techniques taught inthe Statics course. As such, they are helpful to all learning styles. The Statics modules ofVLSM contain 21 test-your-knowledge exercises.

• Design and Analysis Tools

In order to help stimulate higher-order thinking, as in synthesis and evaluation, we havedeveloped two Java-based software tools for rapid development of alternative design modelswith accompanying analysis solutions. Figure 6 shows the Shape Design and Analysis Tool (S-DAT) in the Geometric Properties of Shapes module.

Fig. 6 Demonstration of S-DAT Java applet

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With the help of S-DAT, students are able to generate a drawing model of any two-dimensionalshape that can be formed using the available templates shown in Fig. 6. S-DAT would thenanalyze the model and provide numerical values for geometric properties such as centroid andarea moments of inertia. S-DAT also allows the student to modify the model and to see theeffects on the calculated geometric properties. One important feature that sets these tools apartfrom those previously developed is that they do not simply provide the final answers, but ratherdemonstrate a step-by-step solution sequence consistent with the methods and techniques taughtin the course. Although helpful to all, these tools are of particular interest to sensing, visual, andglobal learners.

Although not as sophisticated as S-DAT, there is also a truss design and analysis tool (T-DAT)in the Trusses, Frames, and Machines module. In that case, students can choose any of the built-in truss models and go through the step-by-step solution sequence for solving for supportreactions as well as for finding the member forces using the method of joints.

• Post a Question

If a student encounters a problem while using VLSM or thinks of a question to ask his/herinstructor, he/she can send an e-mail to his/her instructor using the built-in message window inVLSM. This feature is set up to include the list of all instructors who are teaching Statics in aparticular semester or summer session. Of these questions, those that could benefit otherstudents are reformatted and added to the list of frequently-asked questions mentionedpreviously.

Effectiveness Assessment

The criteria we have established for evaluating the quality of VLSM and its effectiveness onstudent learning are outlined in Table 2 below.

Table 2. Criteria for evaluating the quality and effectiveness of VLSM

Constituency Criteria

Students • Views on VLSM’s content presentation, clarity, and user friendliness.• Preference in using VLSM in addition to / instead of the textbook.• Interest in the course as a result of using VLSM.• Knowledge and comprehension of concepts in Statics.• Skills in analyzing problems and applying solution techniques.

Educators • Views on VLSM’s content and pedagogical style.• Use of VLSM as a preferred tool for in-class concept demonstrations and

example problem discussions.• Willingness to experiment with instructional technology as a result of

having access to VLSM.

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VLSM Related Publications

• Rais-Rohani, M. “On Development, Application and Effectiveness of a Computer BasedTutorial in Engineering Mechanics (Statics),” Proceedings of the 2001 ASEE AnnualConference and Exposition, Albuquerque, NM, June 24-27, 2001.

• Rais-Rohani, M., “On Effectiveness of an Online Tutorial to Enhance Statics Instruction,”Computers in Education Journal, Vol. XI, No. 2, 2001, pp. 38-43.

• Rais-Rohani, M., “VLSM: An Online Tutorial for Solid Mechanics,” Computers inEducation Journal, Vol. XI, No. 1, 2001, pp. 38-44.

• Rais-Rohani, M. and Brown, D., “Development of a Virtual Laboratory for the Study ofMechanics,” Proceedings of the ASEE Annual Conference and Exposition, St. Louis, MO,June 18-21, 2000.

Request to VLSM User Community

In an effort to improve the effectiveness of VLSM both as an asynchronous tutorial and ateaching tool, we solicit feedback from all who have used VLSM in any fashion. Please e-mailyour comments and suggestions to Dr. Masoud Rais-Rohani (masoud@ae.msstate.edu).